TY - JOUR
T1 - QUANTUM KIRWAN MORPHISM AND GROMOV–WITTEN INVARIANTS OF QUOTIENTS III
AU - WOODWARD, C. H.R.I.S.T.
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gauged Gromov–Witten potential of X with the genus zero Gromov–Witten graph potential of X//G. We also give a formula for a solution to the quantum differential equation on X//G in terms of a localized gauged potential for X. These results overlap with those of Givental [14], Lian–Liu–Yau [21], Iritani [20], Coates–Corti–Iritani–Tseng [11], and Ciocan–Fontanine–Kim [7], [8].
AB - This is the third in a sequence of papers in which we construct a quantum version of the Kirwan map from the equivariant quantum cohomology QHG(X) of a smooth polarized complex projective variety X with the action of a connected complex reductive group G to the orbifold quantum cohomology QH(X//G) of its geometric invariant theory quotient X//G, and prove that it intertwines the genus zero gauged Gromov–Witten potential of X with the genus zero Gromov–Witten graph potential of X//G. We also give a formula for a solution to the quantum differential equation on X//G in terms of a localized gauged potential for X. These results overlap with those of Givental [14], Lian–Liu–Yau [21], Iritani [20], Coates–Corti–Iritani–Tseng [11], and Ciocan–Fontanine–Kim [7], [8].
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U2 - 10.1007/s00031-015-9336-7
DO - 10.1007/s00031-015-9336-7
M3 - Article
AN - SCOPUS:84945439812
VL - 20
SP - 1155
EP - 1193
JO - Transformation Groups
JF - Transformation Groups
SN - 1083-4362
IS - 4
ER -